PSI - Issue 68

Gül Demirer et al. / Procedia Structural Integrity 68 (2025) 190–196 G. Demirer and A. Kayran / Procedia Structural Integrity 00 (2024) 000–000

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To find the constant vertical distance D , the lower and upper halves of the course top boundary are considered. The top boundary is a vertical shift of the bottom boundary by D through + y -direction. Using Eq. 3b the lower half of the top boundary is given by y top L = − ρ sinT 0 +  ( ρ − W course 2 ) 2 − ( ρ cosT 0 − x ) 2 + D for − w / 2 ≤ x ≤ 0 . (5) The upper portion can be derived from the centerline equation with a di ff erent radius. Fig. 1c shows that the radius should be ( ρ − ( Dsin φ − W course / 2)) instead of ρ , where φ is the fiber orientation angle at any point. Recall Eq. 3a, y top U = ρ sinT 0 −  ( ρ − ( Dsin φ − W course 2 )) 2 − ( ρ cosT 0 + x ) 2 for 0 ≤ x ≤ w / 2 . (6) The lower and upper halves of the course top boundary intersects at x = 0. Hence Eq. 5 and Eq. 6 are equated at x = 0. Finally, D is obtained as D = 2    ρ sinT 0 −  ( ρ − W course 2 ) 2 − ( ρ cosT 0 ) 2    . (7) In Fig. 2, a course with 8 tows is shown. Blue lines indicate tow boundaries if no tow-drop occurs, black lines depict modified course boundaries, and black dots mark intersections of the upper course boundary with individual tows, which define the boundaries of defects. Green dots indicate defect region corners, created by o ff setting intersection points (black dots) perpendicular to the local fiber orientation based on the coverage percentage. For 0% coverage, a tow is cut when one edge intersects the course boundary; for 100% coverage, both edges must cross the boundary be fore a tow is dropped. Consequently, gaps and overlaps are created according to the coverage percentage, as illustrated in Figs. 2a and 2b.

(a) gaps for 0% coverage

(b) overlaps for 100% coverage

Fig. 2. Procedure for locating gaps and overlaps over the reference course